Subitizing

From the experience of teachers teaching children with a specific deficit in dealing with
numbers (dyscalculia) it was suggested, that these children suffer from an instable sense of
number. They know the digits (the visual signs of numbers) and they know the words for
numbers (the auditory sign for numbers) but they did not associate the number of items
represented by the visual and auditory signs. The idea was that may be they could not develop
this sense of number, because of a visual deficit in their brains.

The corresponding visual capacity is called subitizing (from lat. Subito = immediately).
Subitizing is a basic capacity of the visual system to "see immediately" the number of items
without counting them. A standardized test task for subitizing item numbers from 1-9 was
developed and applied to a large number of control subjects and to children with dyscalculia.

Later the task was also applied to children with dyslexia and other learning problems.

Age Development and Diagnosis

Perfect subitizing is possible for adult subjects up to item numbers of 4 or 5. With increasing
numbers additional time is needed to tell the numbers correctly. For 8 items the rate of
correct responses drops to 80%and is still reasonably high.

Subitizing improves with age until adulthood. Both the basic response time (for item numbers
of 1 and 2) and the effective rate of correct responses (item numbers of 4 and more) improve.
Beyond the age of about 35 years the curves decline.

Diagnosis

Children with dyscalculia exhibit considerable deficits increasing with age.
Even with 1 or 2 items (randomly selected out of 1-9 itms) they need more time as compared
with the controls.

The graph shows the basic response time versus age for two groups.
Considering 4 items and more one can calculate the effective recognition speed as the the
percent number of correct response divided by the response time.

The percent number of subjects failing the range of the age matched controls increases from
about 40% to about 70% with age.

Deficits of subitizing were found also in children with dyslexia. They are about as fast in the
basic reponses but the recognition speed is significantly lower as compared with the controls.

Training

A training of subitizing helps to overcome this deficit. A training device CountTrain was
developed and given to those children, where deficits were encountered. At the beginning the
task was made very easy by selecting only 1 to 3 items and presenting them for lnger times.
Only when the child improved the performance the task was made more difficult by
increasing the maximal number of items and by decreasing the presentation time.

The effect of the training shows a significant improvement of the performance at all ages.

Transfer to Arithmetic

Finally, it was shown, that the training of subitizing transfers to basic mathematical skills as
tested by using the DEMAT+2 (a German test battery commercially available) before and
after the training.
The trained group I gained points, while the waiting group II had no profit from the school
lessons. Only after the waiting group was also allowed to do the training an increase of points
was obtained.